Numerical studies for the variable-order nonlinear fractional wave equation

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
N. Sweilam ◽  
M. Khader ◽  
H. Almarwm
Keyword(s):  
Wave Equation ◽  
Stability Analysis ◽  
Numerical Scheme ◽  
Numerical Test ◽  
Variable Order ◽  
Fractional Wave Equation ◽  
Numerical Studies ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Explicit Finite Difference Method

AbstractIn this paper, the explicit finite difference method (FDM) is used to study the variable order nonlinear fractional wave equation. The fractional derivative is described in the Riesz sense. Special attention is given to study the stability analysis and the convergence of the proposed method. Numerical test examples are presented to show the efficiency of the proposed numerical scheme.

scholarly journals Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Nasser Hassan Sweilam ◽  
Taghreed Abdul Rahman Assiri
Keyword(s):  
Wave Equation ◽  
Truncation Error ◽  
Source Term ◽  
Numerical Test ◽  
Space Time ◽  
Variable Order ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Variable Order Fractional Derivative ◽  
Explicit Finite Difference Method

The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. The concept of variable order fractional derivative is considered in the sense of Caputo. The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presented.

scholarly journals Error Analysis of An Explicit Finite Difference Approximation for the Space Fractional Wave Equations

2012 ◽  
Vol 17 (2) ◽  
pp. 245
Author(s):  
N.H. Sweilam ◽  
T.A. Assiri
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Error Analysis ◽  
Wave Equations ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Explicit Finite Difference ◽  
The Stability

In this paper, the space fractional wave equation (SFWE) is numerically studied, where the fractional derivative is defined in the sense of Caputo. An explicit finite difference approximation (EFDA) for SFWE is presented. The stability and the error analysis of the EFDA are discussed. To demonstrate the effectiveness of the approximated method, some test examples are presented.   

scholarly journals Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives

2016 ◽  
Vol 26 (3) ◽  
pp. 429-435 ◽  
Author(s):  
Roman I. Parovik
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Fractional Derivatives ◽  
Stability And Convergence ◽  
Variable Order ◽  
The Difference ◽  
Explicit Finite Difference ◽  
The Stability ◽  
Variable Order Fractional Derivatives

Abstract The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.

scholarly journals Convergence and stability analysis of an explicit finite difference method for 2-dimensional reaction-diffusion equations

1994 ◽  
Vol 36 (2) ◽  
pp. 234-241 ◽  
Author(s):  
Nian Li ◽  
Joseph Steiner ◽  
Shimin Tang
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Reaction Diffusion Equations ◽  
Conditional Convergence ◽  
Convergence And Stability ◽  
Explicit Finite Difference ◽  
Convergence And Stability Analysis ◽  
Explicit Finite Difference Method

AbstractThe convergence and stability analysis of a simple explicit finite difference method is studied in this paper. Conditional convergence and stability theorems for this method are given. We have also proved that this scheme is stable in a much stronger sense.

scholarly journals Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays

2021 ◽  
pp. 6-6
Author(s):  
Mesfin Woldaregay ◽  
Worku Aniley ◽  
Gemechis Duressa
Keyword(s):  
Numerical Scheme ◽  
Numerical Test ◽  
Singularly Perturbed ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Solution Methods ◽  
Solution Bound ◽  
The Stability ◽  
Delay Differential ◽  
Exponential Boundary Layer

This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.

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